Ideally, programming propagators as implementations of
constraints should be an entirely declarative specification process
for a large class of constraints: a high-level declarative
specification is automatically translated into an efficient
propagator. This paper introduces the use of existential
monadic second-order logic as declarative
specification language for finite set propagators. The approach taken in
the paper is to automatically derive projection propagators (involving a
single variable only) implementing
constraints described by formulas. By this, the paper
transfers the ideas of indexicals to finite set constraints
while considerably increasing the level of
abstraction available with indexicals. The paper proves soundness
and completeness of the derived propagators and presents a runtime
analysis, including techniques for efficiently executing projectors
for n-ary constraints.